Man's physical universe



A tone rich in overtones is carried to the ear by a mixture of compressional

waves of different frequencies and different intensities,

traveling in

the same direction.

There Is a Vast Range of Frequencies for Sound Waves.

Pitch can be expressed in


terms of frequency by comparison with

sounds created by mechanical means that produce a known number of

vibrations per second.

If a card is held against the serrated edge of a revolving disk, it will

produce vibrations whose frequency depends upon the rate at which

the disk moves.

Of course, pitch can be obtained from records produced by the phonautograph,

the phonodeik, and similar instruments, but it can also be

determined by means of tuning forks which vibrate with known frequencies.

Two sound waves whose frequencies are 250 and 251 per

second will be in phase ^ at one instant and produce the maximum

sound, but half a second later they will be opposite in phase, and less

sound will be heard because of interference. At the end of the second

they will be in phase again, and the sound will again be heard.

If the

frequencies had been 250 and 252, there would have been two of these

variations of loudness, otherwise known as "beats." In comparing

the pitch of a vibration whose pitch is not known with a known pitch,

the difference in the frequency between the tones is equal to the number

of beats heard per second. This method of tuning instruments is

The charm of music produced

sufficiently accurate for most purposes.

by bells is due in part to the beats that accompany their tones.

Middle C on the piano has a frequency of 258.7 complete vibrations

(cycles) per second on the International Scale. An octave consists of

the range of pitch between any two frequencies in which one is twice

the other. The piano has a range from 27.2 to 4138.4 complete vibrations

per second. The range for the organ is 16 to 4138 complete vibrations

per second. The organ pipe giving 16 complete vibrations per

second is about 32 feet long. A few organs have pipes 64 feet long that

give only 8 complete vibrations per second. The organ pipe that has a

frequency of 4138 complete vibrations per second is only 1 Yi inches long.

There are upper and lower limits to the pitch of notes which can be

heard by the ear, but both limits vary with different persons. Few


Phase — Imagine two boys swinging in two identical swings placed side by side, the

period in each case being the same. If the two boys reach the same relative positions

at the same time, they are in phase. If they are opposite each other when they reach their

greatest height, there is a phase difference of 180°. while, if one boy is at the height of his

swing while the other boy is at the lowest point of his swing, there is a phase difference of

90°. Any other combination of swings which are out of phase could be worked out.

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